{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# ME424 Modern Control and Estimation\n",
    "## Homework #1"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "雷天健 12132267"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 1. System Installation"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "![image-20210912205240033](image-20210912205240033.png)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 2. Python Basics\r\n",
    "Please carefully study the Python tutorial posted on the class website, and\r\n",
    "complete the following questions."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(a) Print the length of the string ”Hello, Python!”."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "s = \"Hello,Python!\"\n",
    "print(len(s))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "13\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(b)  Create a ’while’ loop that sums the numbers from 1 to 100."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "i = 1\n",
    "sum = 0\n",
    "while i <= 100:\n",
    "    sum += i\n",
    "    i += 1\n",
    "print(sum)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "5050\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(c) Make a program that prints the fruits in the set one by one: fruit list = [’apple’, ’pair’, ’banana’, ’orange’, ’watermelon’].\r\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "fruit_list = ['apple', 'pair', 'banana', 'orange', 'watermelon']\n",
    "for i in fruit_list:\n",
    "    print(i)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "apple\n",
      "pair\n",
      "banana\n",
      "orange\n",
      "watermelon\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(d) Define a class which has the two methods below:\r\n",
    "- getString(): to get a string from console input.\r\n",
    "- printString(): to print the string in upper case.\r\n",
    "\r\n",
    "Then write a simple program to test the class methods."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "import os\n",
    "class Test:\n",
    "\n",
    "    def __init__(self):\n",
    "        self.text = \"\"\n",
    "        self.getString()\n",
    "\n",
    "    def getString(self):\n",
    "        self.text = input(\"input: \")\n",
    "\n",
    "    def printString(self):\n",
    "        print(self.text.upper())\n",
    "\n",
    "t = Test()\n",
    "t.printString()"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "TEST\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 3. Linear Algebra with Python\r\n",
    "In this class, we will have a lot of work to do with linear\r\n",
    "algebra. It is important to use Python to complete the linear algebra task. Let’s get familiar\r\n",
    "with it now."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "$$\r\n",
    "    A = \\begin{bmatrix}\r\n",
    "            1 & -2 & 4 \\\\\r\n",
    "            1 & -1 & 1 \\\\\r\n",
    "            1 & 0 & 0 \\\\\r\n",
    "            1 & 1 & 1 \\\\\r\n",
    "            1 & 2 & 4\r\n",
    "        \\end{bmatrix}  \\quad\r\n",
    "        B = \\begin{bmatrix}\r\n",
    "        1 & 2 & 3 \\\\\r\n",
    "        1 & 2 & 3 \\\\\r\n",
    "        1 & 2 & 3 \\\\\r\n",
    "        1 & 2 & 3 \\\\\r\n",
    "        1 & 2 & 3 \\\\\r\n",
    "    \\end{bmatrix}\r\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(a) Print the two matrices $A$ and $B$."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "import numpy as np\n",
    "A = np.array([[1, -2, 4], [1, -1, 1], [1, 0, 0], [1, 1, 1], [1, 2, 4]])\n",
    "B = np.array([[1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3]])\n",
    "\n",
    "print(A)\n",
    "print(B)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[ 1 -2  4]\n",
      " [ 1 -1  1]\n",
      " [ 1  0  0]\n",
      " [ 1  1  1]\n",
      " [ 1  2  4]]\n",
      "[[1 2 3]\n",
      " [1 2 3]\n",
      " [1 2 3]\n",
      " [1 2 3]\n",
      " [1 2 3]]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(b) Print the second row of $A$ and the third column of $B$."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "print(A[1, :])\n",
    "print(B[:, 2])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[ 1 -1  1]\n",
      "[3 3 3 3 3]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(c) Print the results of $A + B$ and $A − B$."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "print(A + B)\n",
    "print(A - B)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[2 0 7]\n",
      " [2 1 4]\n",
      " [2 2 3]\n",
      " [2 3 4]\n",
      " [2 4 7]]\n",
      "[[ 0 -4  1]\n",
      " [ 0 -3 -2]\n",
      " [ 0 -2 -3]\n",
      " [ 0 -1 -2]\n",
      " [ 0  0  1]]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(d) Construct a new 5 × 6 matrix $[A, B]$ by appending $B$ to the right of matrix $A$."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "print(np.hstack((A, B)))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[ 1 -2  4  1  2  3]\n",
      " [ 1 -1  1  1  2  3]\n",
      " [ 1  0  0  1  2  3]\n",
      " [ 1  1  1  1  2  3]\n",
      " [ 1  2  4  1  2  3]]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(e) Compute $A^TB$."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "source": [
    "print(np.dot(A.T, B))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[ 5 10 15]\n",
      " [ 0  0  0]\n",
      " [10 20 30]]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4. Matplotlib"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(a) Plot a unit circle."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "source": [
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0, np.pi * 2, 500)\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(np.cos(t), np.sin(t))\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "(b) Plot a plus sign ”+” inside the unit circle, for which the horizontal line and vertical line\r\n",
    "both touches the circle."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "t = np.linspace(0, np.pi * 2, 500)\n",
    "h_x = np.linspace(-1, 1, 500)\n",
    "h_y = np.zeros(500)\n",
    "\n",
    "v_x = np.zeros(500)\n",
    "v_y = np.linspace(-1, 1, 500)\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(np.cos(t), np.sin(t), h_x, h_y, v_x, v_y)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  }
 ],
 "metadata": {
  "orig_nbformat": 4,
  "language_info": {
   "name": "python",
   "version": "3.6.9",
   "mimetype": "text/x-python",
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "pygments_lexer": "ipython3",
   "nbconvert_exporter": "python",
   "file_extension": ".py"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.6.9 64-bit"
  },
  "interpreter": {
   "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}